scholarly journals Normal forms for skew-symmetric matrices and Hamiltonian systems with first integrals linear in momenta

1988 ◽  
Vol 104 (3) ◽  
pp. 910-910 ◽  
Author(s):  
G. Thompson
Keyword(s):  
Hamiltonian Systems ◽  
Normal Forms ◽  
First Integrals ◽  
Symmetric Matrices

First integrals and Darboux polynomials of natural polynomial Hamiltonian systems

2010 ◽  
Vol 374 (47) ◽  
pp. 4746-4748 ◽  
Author(s):  
Isaac A. García ◽  
Maite Grau ◽  
Jaume Llibre
Keyword(s):  
Hamiltonian Systems ◽  
First Integrals ◽  
Darboux Polynomials

scholarly journals PERIODIC FIRST INTEGRALS FOR HAMILTONIAN SYSTEMS OF LIE TYPE

2011 ◽  
Vol 08 (06) ◽  
pp. 1169-1177 ◽  
Author(s):  
RUBEN FLORES ESPINOZA
Keyword(s):  
Hamiltonian Systems ◽  
Nonlinear Oscillator ◽  
Original System ◽  
First Integrals ◽  
Time Dependent ◽  
Existence Problem ◽  
Adjoint Group ◽  
Killing Form ◽  
Modern Physics ◽  
Existence Of Periodic Solutions

In this paper, we study the existence problem of periodic first integrals for periodic Hamiltonian systems of Lie type. From a natural ansatz for time-dependent first integrals, we refer their existence to the existence of periodic solutions for a periodic Euler equation on the Lie algebra associated to the original system. Under different criteria based on properties for the Killing form or on exponential properties for the adjoint group, we prove the existence of Poisson algebras of periodic first integrals for the class of Hamiltonian systems considered. We include an application for a nonlinear oscillator having relevance in some modern physics applications.

On First Integrals of Linear Hamiltonian Systems

2018 ◽  
Vol 98 (3) ◽  
pp. 616-618 ◽  
Author(s):  
A. B. Zheglov ◽  
D. V. Osipov
Keyword(s):  
Hamiltonian Systems ◽  
First Integrals ◽  
Linear Hamiltonian Systems

scholarly journals Generic super-exponential stability of invariant tori in Hamiltonian systems

2010 ◽  
Vol 31 (5) ◽  
pp. 1287-1303 ◽  
Author(s):  
ABED BOUNEMOURA
Keyword(s):  
Hamiltonian System ◽  
Exponential Stability ◽  
Fixed Points ◽  
Hamiltonian Systems ◽  
Normal Forms ◽  
Invariant Tori ◽  
The Other ◽  
New Method ◽  
Stable Invariant

AbstractIn this article, we consider solutions that start close to some linearly stable invariant tori in an analytic Hamiltonian system, and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms with a new method for obtaining generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will focus mainly on the neighbourhood of elliptic fixed points, since with our approach the other cases can be treated in a very similar way.

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